Question 497161: A stained - glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 4 ft2 of glass is to be used, find the height h. (Round your answer to the nearest hundredth.) Answer by solver91311(16868) (Show Source):
If you mean that the overall area of both the rectangle and the surmounting semi-circle is supposed to be 4 ft², then this is mighty weird looking stained glass window. Since you didn't provide a dimension for the diameter of the semicircle, I have to assume that it is the same as the width of the rectangle. I'm also assuming that is the missing dimension of the rectangle since it cannot possibly be the overall height of the window. The area of a semicircle with a diameter of 3 feet and therefore a radius of 1.5 feet is . That means only of the given area remains for the rectangle. Divided by 3, that leaves a height of less than feet for the rectangle part of the window -- not even 2 inches. Standing back, you probably wouldn't notice that there was a rectanglual part of the window.
My calculator said it, I believe it, that settles it